Question

Use Gauss's approach to find a formula for the sum of the even numbers from 2+4+6+...+2n . The formula will be an expression involving n.

Answer 1

When Friedrich Gauss was about 8 years old, his teacher asked the class to add numbers 1,2,3....100, before they could go out and play. Gauss sat down and gave his answer in about a minute. This is how he worked it out:

Say
sum=1+2+3+4+..............+100
He put it backwards, so
sum=100+99+98+97.......+1
Since 1+100=101, 2+99=101, ....100+1=101, for each and every one of the hundred numbers, so
2 times sum = 100*101=10100
sum = 5050.

That's how he did it at eight years old, so you can do yours too, for 2+ 4+ 6, ....+2n.

Yes, this is the same Gauss as in Gauss Elimination.

:)

Answer 2

When the "n" is amount of numbers you want to add up.
"a1" is first number and "an" is the last number.

"n" is a subscript